Route-based transportation network design

Given shipment demand and driving regulations, a consolidation carrier has to make decisions on how to route both shipments and drivers at minimal cost. The traditional way to formulate and solve these problems is through the use of two-step models. This thesis presents a heuristic algorithm to solve an integrated model that can provide superior solutions. The algorithm combines a slope scaling initialization phase and tabu search to find high-quality solutions. The performance of the proposed heuristic is benchmarked against a commercial solver and these results indicate that the proposed method is able to produce better quality solutions for the similar solution time

A Computational study of branching rules for multi-commodity fixed-charged network flow problems

Branch and bound based algorithms are used by many commercial mixed integer programming solvers for solving complex optimization problems. In a branch and bound based method, a feasible region is divided into smaller sub-problems. This is called branching and various branching strategies have been developed to improve the performance of branch and bound based algorithms. However, their performance has primarily been studied on general mixed integer programs. Thus, in the first phase of this thesis, we study the performance of these branching strategies on a specific, structured mixed integer program, the capacitated multi-commodity fixed charge network flow (MCFCNF) problem. We also develop new branching strategies using the pool of available feasible solutions for solving the mixed integer program for MCFCNF. We present the computational results for testing various branching rules with four different variants of the network design problem studied with SCIP and GLPK mathematical solvers

Improved load plan design through integer programming based local search

We present integer programming models of the service network design problem faced by less-than-truckload (LTL) freight transportation carriers and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers and thus explicitly recognize the efficiencies presented by backhaul lanes. The solution approach can generate the traditional service network designs commonly used by LTL carriers but also enables the construction of designs that allow more flexibility, e.g., that allow freight routes to vary by day of week. An iterative improvement scheme is employed that searches a large neighborhood, each iteration using an integer program. Computational experiments using data from a large U.S. carrier demonstrate that the proposed modeling and solution approach has the potential to generate significant cost savings. 2013 INFORMS

Soft clustering-based scenario bundling for a progressive hedging heuristic in stochastic service network design

We present a method for bundling scenarios in a progressive hedging heuristic (PHH) applied to stochastic service network design, where the uncertain demand is represented by a finite number of scenarios. Given the number of scenario bundles, we first calculate a vector of probabilities for every scenario, which measures the association strength of a scenario to each bundle center. This membership score calculation is based on existing soft clustering algorithms such as Fuzzy C-Means (FCM) and Gaussian Mixture Models (GMM). After obtaining the probabilistic membership scores, we propose a strategy to determine the scenario-to-bundle assignment. By contrast, almost all existing scenario bundling methods such as K-Means (KM) assume before the scenario-to-bundle assignment that a scenario belongs to exactly one bundle, which is equivalent to requiring that the membership scores are Boolean values. The probabilistic membership scores bring many advantages over Boolean ones, such as the flexibility to create various degrees of overlap between scenario bundles and the capability to accommodate scenario bundles with different covariance structures. We empirically study the impacts of different degrees of overlap and covariance structures on PHH performance by comparing PHH based on FCM/GMM with that based on KM and the cover method, which represents the state-of-the-art scenario bundling algorithm for stochastic network design. The solution quality is measured against the lower bound provided by CPLEX. The experimental results show that, GMM-based PHH yields the best performance among all methods considered, achieving nearly equivalent solution quality in a fraction of the run-time of the other methods

COMPACT FORMULATION OF MULTICOMMODITY NETWORK FLOWS WITH APPLICATIONS TO THE BACKHAUL PROFIT MAXIMIZATION PROBLEM AND FIXED CHARGE NETWORK FLOW PROBLEM

The triples formulation is a compact formulation of multicommodity network flow problems that provides a different representation of flow than the traditional and widely used node-arc and arc-path approaches. In the literature, the triples formulation has been applied successfully to the maximum concurrent flow problem and to a network optimization problem with piecewise linear convex costs. This dissertation applies the triples formulation to the backhaul profit maximization problem (BPMP) and the fixed charge network flow problem (FCNF). It is shown that the triples representation of multicommodity flow significantly reduces the number of variables and constraints in the mixed integer programming formulations of the BPMP and FCNF. For the BPMP, this results in significantly faster solution times. For dense problem instances, the triples-based formulation of FCNF is found to produce better solutions than the node-arc formulation early in the branch-and-bound process. This observation leads to an effective hybrid method which combines the respective advantages of the smaller size of the triples formulation and the stronger linear programming relaxation of the node-arc formulation. In addition to empirical studies, the dissertation presents new theoretical results supporting the equivalence of the triples formulation to the node-arc and arc-path formulations. The dissertation also proposes a multi-criteria Composite Index Method (CIM) to compare the performance of alternative integer programming formulations of an optimization problem. Using the CIM, the decision maker assigns weights to problem instance sizes and multiple performance measures based on their relative importance for the given application. The weighting scheme is used to produce a single number that measures the relative improvement of one alternative over the other and provides a method to select the most effective approach when neither one dominates the other when tested on different sizes of problem instances. The dissertation demonstrates a successful application of the CIM to evaluate a series of eleven techniques for improving the node-arc and triples formulations of the BPMP previously proposed in the literature

Improved load plan design through integer programming based local search. Transportation Science

Abstract We present integer programming models of the service network design problem faced by lessthan-truckload (LTL) freight transportation carriers, and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers, and thus explicitly recognize the efficiencies presented by backhaul lanes. The solution approach can generate the traditional service network designs commonly used by LTL carriers, but also enables the construction of designs that allow more flexibility, e.g., that allow freight routes to vary by day of week. An iterative improvement scheme is employed which searches a large neighborhood each iteration using an integer program. Computational experiments using data from a large U.S. carrier demonstrate that the proposed modeling and solution approach has the potential to generate significant cost savings

A computational study of practical issues arising in short-term scheduling of a multipurpose facility

This thesis focuses on two important considerations when solving short term scheduling problems for multipurpose facilities: deciding when rescheduling should be performed and choosing efficient time representations for the scheduling problems. This class of scheduling problems is of practical importance as it may be used for scheduling chemical production facilities, flexible manufacturing systems, and analytical services facilities, among others. In these cases, improving the efficiency of scheduling operations may lead to increased yield, or reduced makespan, resulting in greater profits or customer satisfaction. Therefore, efficiently solving these problems is of great practical interest. One aspect of real world implementations of these problems is the presence of uncertainty, such as in the form of new jobs arriving, or a machine breaking down. In these cases, one may want or need to reschedule operations subject to the new disturbance. An investigation into how often to perform these reschedulings is addressed in the first part of the thesis. When formulating these problems, one must also choose a time representation for executing scheduling operations over. A dynamic approach is proposed in the second part of the thesis which we show can potentially yield substantial computational savings when scheduling over large instances. The first part of this thesis addresses the question of when to reschedule operations for a facility that receives new jobs on a daily basis. Through computational experiments that vary plant parameters, such as the load and the capacity of a facility, we investigate the effects these parameters have on plant performance under periodic rescheduling. These experiments are carried out using real data from an industrial-scale facility. The results show that choosing a suitable rescheduling policy depends on some key plant parameters. In particular, by modifying various parameters of the facility, the performance ranking of the various rescheduling policies may be reversed compared to the results obtained with nominal parameter values. This highlights the need to consider both facility characteristics and what the crucial objective of the facility is when selecting a rescheduling policy. The second part of this thesis deals with the issue of deciding which timepoints to include in our model formulations. In general, adding more timepoints to the model will offer more flexibility to the solver and hence result in more accurate schedules. However, these extra timepoints will also increase the size of the model and accordingly the computational cost of solving the model. We propose an iterative framework to refine an initial coarse uniform discretization, by adding key timepoints that may be most beneficial, and removing timepoints which are unnecessary from the model. This framework is compared against existing static discretizations using computational experiments on an analytical services facility. The results of these experiments demonstrate that when problems are sufficiently large, our proposed dynamic method is able to achieve a better tradeoff between objective value and CPU time than the currently used discretizations in the literature